A Remark on Euclid's Theorem on the Infinitude of the Primes.

The article focuses on the application of the theory of finite abelian groups to prove that there are certain numbers of primes in a given initial segment of the natural numbers, which was published in the 1889 paper of Joseph Perott. It says that the idea of Perott was called a remark on Euclid's theorem and the proof was based on two simple lemmas such as homomorphism and isomorphism. Moreover, an earlier paper where Perott proved a substantial result of the theorem is also discussed.